ManukaAnalysis

Import and Arrange Data

“Full.xlsx”, sheet “Full” contains measurement information from sampling with the Dualex (https://www.force-a.com/en/capteurs-optiques-optical-sensors/dualex-scientific-chlorophyll-meter/), including;

• Surface content of chlorophyll in \(g/cm^2\) (Chl)

• Epidermal Flavoid content in absorbance units; Flavonol(Flav) and Anthocyanin(Anth)

• Nitrogen Balance Index status is calculated using Chlorophyll and Flavonol values automatically (NBI)

It also contains information about the block position, the leaf height information, and presense or absence of flowering

Sheet “Dup” contains only the replicated samples

# Import Data Measures
Data <-read.xlsx("Full.xlsx", sheetName ="Full")
head(Data)

##   Collection.Day Allocation Block Column Row group Group.ID Tree.ID Rep.
## 1              4         CG     0      0   0    20       OG      CG    N
## 2              4         CG     0      0   0    20       OG      CG    N
## 3              4         CG     0      0   0    20       OG      CG    N
## 4              4         CG     0      0   0    20       OG      CG    N
## 5              4         CG     0      0   0    20       OG      CG    N
## 6              4         CG     0      0   0    20       OG      CG    N
##   measure Height Flower    Chl  Flav  Anth   NBI
## 1       9      H      Y 28.220 2.418 0.205 11.67
## 2       3      L      Y 27.958 2.298 0.691 12.17
## 3      11      H      Y 33.727 2.458 0.527 13.72
## 4       4      L      Y 25.938 1.758 0.172 14.76
## 5      10      H      Y 36.205 2.283 0.270 15.86
## 6       6      M      Y 34.332 2.115 0.150 16.23

Data$Column = as.factor(Data$Column)
Data$Row = as.factor(Data$Row)

# Import Replicate Data
Dup <-read.xlsx("Full.xlsx", sheetName ="Dup")
head(Dup)

##   Collection.Day group Group.ID Tree.ID Rep. measure Height   Chl  Flav
## 1            2.0    23       60   IN4DV   Y1       1      L 1.916 2.363
## 2            1.5     3        1   IN4BT   Y1       1      L 3.124 2.300
## 3            2.0    17       54   IN4DL   Y2       2      L 3.414 1.826
## 4            1.5    32       28   IN4CP   Y2       2      L 4.097 1.943
## 5            2.0     9       46   IN4DC   Y1       1      L 4.909 1.928
## 6            1.5     5        3   IN4BW   Y1       1      L 4.924 1.848
##    Anth  NBI
## 1 0.174 0.81
## 2 0.191 1.36
## 3 0.112 1.87
## 4 0.051 2.11
## 5 0.103 2.55
## 6 0.165 2.66

#Isolate Crimson Glory Outgroup
CG = Data[c(1:11),]

#Isolate East Cape 201 Parent
EC201 = Data[c(12:21),]

#Isolate East Cape 103 Parent
EC103 = Data[c(22:33),]

#Isolate Offspring from the Parental Cross
F1 = Data[c(34:1825),]

Replicate Data Overview

##                Min.     1st Qu.      Median        Mean     3rd Qu.
## RepAnth  0.00100000  0.06500000  0.09850000  0.09799367  0.12525000
## RepChl   1.91600000 25.82475000 36.02700000 35.76269937 46.61000000
## RepFlav  1.05600000  1.76775000  1.99400000  1.96720570  2.19725000
## RepNBI   0.81000000 12.70250000 18.19000000 18.73398734 24.45750000
##                Max.
## RepAnth  0.25400000
## RepChl  59.67400000
## RepFlav  2.71400000
## RepNBI  43.49000000

Replicate Group means

## # A tibble: 2 x 5
##   Rep.    Anth   Chl  Flav   NBI
##   <fct>  <dbl> <dbl> <dbl> <dbl>
## 1 Y1    0.0983  34.9  1.98  18.2
## 2 Y2    0.0977  36.6  1.95  19.2

Anthocyanin Replicate Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Chlorphyll Replicate Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Flavonol Replicate Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Nitrogen Balance Replicate Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

There is no statistically significant differences between the two groups of measurements, this is a good sign indicative of the accuracy of the Dualex.

ANOVA of Replicates

• Anothcyanin

## Analysis of Variance Table
## 
## Response: Dup$Anth
##            Df  Sum Sq   Mean Sq F value Pr(>F)
## Dup$Rep.    1 0.00003 0.0000304  0.0151 0.9023
## Residuals 314 0.63303 0.0020160

## 
## Call:
## lm(formula = Dup$Anth ~ Dup$Rep.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.097302 -0.032682  0.000818  0.027568  0.156318 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.0983019  0.0035608  27.607   <2e-16 ***
## Dup$Rep.Y2  -0.0006204  0.0050518  -0.123    0.902    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0449 on 314 degrees of freedom
## Multiple R-squared:  4.802e-05,  Adjusted R-squared:  -0.003137 
## F-statistic: 0.01508 on 1 and 314 DF,  p-value: 0.9023

• Chlorophyll

## Analysis of Variance Table
## 
## Response: Dup$Chl
##            Df Sum Sq Mean Sq F value Pr(>F)
## Dup$Rep.    1    218  218.33   1.033 0.3102
## Residuals 314  66366  211.36

## 
## Call:
## lm(formula = Dup$Chl ~ Dup$Rep.)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.185  -9.724   0.252  10.891  24.737 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   34.937      1.153  30.302   <2e-16 ***
## Dup$Rep.Y2     1.662      1.636   1.016     0.31    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.54 on 314 degrees of freedom
## Multiple R-squared:  0.003279,   Adjusted R-squared:  0.0001048 
## F-statistic: 1.033 on 1 and 314 DF,  p-value: 0.3102

• Flavonol

## Analysis of Variance Table
## 
## Response: Dup$Flav
##            Df  Sum Sq  Mean Sq F value Pr(>F)
## Dup$Rep.    1  0.0521 0.052129  0.6506 0.4205
## Residuals 314 25.1596 0.080126

## 
## Call:
## lm(formula = Dup$Flav ~ Dup$Rep.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.89828 -0.19930  0.01538  0.23197  0.73403 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.97997    0.02245  88.200   <2e-16 ***
## Dup$Rep.Y2  -0.02569    0.03185  -0.807    0.421    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2831 on 314 degrees of freedom
## Multiple R-squared:  0.002068,   Adjusted R-squared:  -0.00111 
## F-statistic: 0.6506 on 1 and 314 DF,  p-value: 0.4205

• Nitrogen

## Analysis of Variance Table
## 
## Response: Dup$NBI
##            Df  Sum Sq Mean Sq F value Pr(>F)
## Dup$Rep.    1    82.5  82.530   1.115 0.2918
## Residuals 314 23241.0  74.016

## 
## Call:
## lm(formula = Dup$NBI ~ Dup$Rep.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.4162  -5.9683  -0.7512   5.5938  24.2417 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  18.2262     0.6823  26.714   <2e-16 ***
## Dup$Rep.Y2    1.0221     0.9680   1.056    0.292    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.603 on 314 degrees of freedom
## Multiple R-squared:  0.003538,   Adjusted R-squared:  0.000365 
## F-statistic: 1.115 on 1 and 314 DF,  p-value: 0.2918

The absence of statistically significant results indicates that our replicates are likely to be consistent.

Allocation Data Overview

##                Min.     1st Qu.      Median        Mean     3rd Qu.
## AllAnth  0.00100000  0.06800000  0.09600000  0.09772877  0.12400000
## AllChl   0.13000000 24.10200000 36.21000000 35.21443342 46.82300000
## AllFlav  1.05600000  1.80600000  1.97800000  1.96440493  2.12800000
## AllNBI   0.07000000 12.14000000 18.64000000 18.34807123 24.44000000
##                Max.
## AllAnth  0.69100000
## AllChl  59.90500000
## AllFlav  2.86100000
## AllNBI  49.17000000

Allocation Group Means

## # A tibble: 4 x 5
##   Allocation   Anth   Chl  Flav   NBI
##   <fct>       <dbl> <dbl> <dbl> <dbl>
## 1 CG         0.258   36.0  2.17  16.7
## 2 EC103      0.0588  52.6  1.60  33.1
## 3 EC201      0.0779  52.6  1.71  31.7
## 4 F1         0.0971  35.0  1.97  18.2

Boxplots Comparing Mean, Median and Measurement Distributions of the Allocation Groups

Allocation ANOVAs

• Anthocyanin

## Analysis of Variance Table
## 
## Response: Data$Anth
##                   Df Sum Sq  Mean Sq F value    Pr(>F)    
## Data$Allocation    3 0.3040 0.101343  47.474 < 2.2e-16 ***
## Residuals       1821 3.8873 0.002135                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Data$Anth ~ Data$Allocation)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.15064 -0.02912 -0.00112  0.02688  0.43336 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           0.25764    0.01393  18.494   <2e-16 ***
## Data$AllocationEC103 -0.19880    0.01929 -10.308   <2e-16 ***
## Data$AllocationEC201 -0.17974    0.02019  -8.903   <2e-16 ***
## Data$AllocationF1    -0.16052    0.01397 -11.487   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0462 on 1821 degrees of freedom
## Multiple R-squared:  0.07254,    Adjusted R-squared:  0.07101 
## F-statistic: 47.47 on 3 and 1821 DF,  p-value: < 2.2e-16

• Chlorophyll

## Analysis of Variance Table
## 
## Response: Data$Chl
##                   Df Sum Sq Mean Sq F value    Pr(>F)    
## Data$Allocation    3   6742 2247.21  9.9149 1.748e-06 ***
## Residuals       1821 412728  226.65                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Data$Chl ~ Data$Allocation)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.866 -10.918   1.121  11.493  24.909 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            36.028      4.539   7.937 3.58e-15 ***
## Data$AllocationEC103   16.564      6.284   2.636  0.00847 ** 
## Data$AllocationEC201   16.578      6.578   2.520  0.01181 *  
## Data$AllocationF1      -1.032      4.553  -0.227  0.82066    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.05 on 1821 degrees of freedom
## Multiple R-squared:  0.01607,    Adjusted R-squared:  0.01445 
## F-statistic: 9.915 on 3 and 1821 DF,  p-value: 1.748e-06

• Flavonol

## Analysis of Variance Table
## 
## Response: Data$Flav
##                   Df  Sum Sq Mean Sq F value    Pr(>F)    
## Data$Allocation    3   2.713 0.90423  14.755 1.708e-09 ***
## Residuals       1821 111.598 0.06128                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Data$Flav ~ Data$Allocation)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9110 -0.1568  0.0110  0.1610  0.8940 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.16945    0.07464  29.065  < 2e-16 ***
## Data$AllocationEC103 -0.56962    0.10334  -5.512 4.05e-08 ***
## Data$AllocationEC201 -0.45865    0.10816  -4.240 2.34e-05 ***
## Data$AllocationF1    -0.20245    0.07487  -2.704  0.00691 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2476 on 1821 degrees of freedom
## Multiple R-squared:  0.02373,    Adjusted R-squared:  0.02212 
## F-statistic: 14.75 on 3 and 1821 DF,  p-value: 1.708e-09

• Nitrogen

## Analysis of Variance Table
## 
## Response: Data$Chl
##                   Df Sum Sq Mean Sq F value    Pr(>F)    
## Data$Allocation    3   6742 2247.21  9.9149 1.748e-06 ***
## Residuals       1821 412728  226.65                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Data$NBI ~ Data$Allocation)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.1144  -6.1044   0.3556   6.0656  30.9856 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            16.739      2.540   6.591 5.72e-11 ***
## Data$AllocationEC103   16.404      3.516   4.665 3.31e-06 ***
## Data$AllocationEC201   14.949      3.681   4.062 5.08e-05 ***
## Data$AllocationF1       1.445      2.548   0.567    0.571    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.424 on 1821 degrees of freedom
## Multiple R-squared:  0.03353,    Adjusted R-squared:  0.03194 
## F-statistic: 21.06 on 3 and 1821 DF,  p-value: 2.069e-13

F1 Samples (Approx 3 years) appear more similar to that of the Crimson Glory plant than either/both parents - this is possibly due to age effects as CG is likely more similar in this regard being shorter (No age confirmed). ANOVAs incidate there is significant differences between the allocations - this is to be expected.

Parent Tree Data Overview

##              Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
## ParAnth  0.004000  0.048250  0.058000  0.067500  0.086750  0.156000
## ParChl  30.722000 50.356750 55.739000 52.598909 57.794750 59.757000
## ParFlav  1.293000  1.475000  1.594000  1.650273  1.821000  2.138000
## ParNBI  14.370000 29.872500 34.025000 32.481818 35.892500 44.880000

Parent Tree Means

## # A tibble: 2 x 5
##   Tree.ID   Anth   Chl  Flav   NBI
##   <fct>    <dbl> <dbl> <dbl> <dbl>
## 1 EC103   0.0588  52.6  1.60  33.1
## 2 EC201   0.0779  52.6  1.71  31.7

Anthocyanin Parent Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Chlorophyll Parent Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Flavonol Parent Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Nitrogen Parent Plots

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Parent t.tests

• Anthocyanin

## 
##  Welch Two Sample t-test
## 
## data:  Parent$Anth by Parent$Tree.ID
## t = -1.2283, df = 19.107, p-value = 0.2342
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.05154327  0.01340994
## sample estimates:
## mean in group EC103 mean in group EC201 
##          0.05883333          0.07790000

• Chlorophyll

## 
##  Welch Two Sample t-test
## 
## data:  Parent$Chl by Parent$Tree.ID
## t = -0.003842, df = 17.804, p-value = 0.997
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -7.830954  7.802387
## sample estimates:
## mean in group EC103 mean in group EC201 
##            52.59242            52.60670

• Flavonol

## 
##  Welch Two Sample t-test
## 
## data:  Parent$Flav by Parent$Tree.ID
## t = -1.141, df = 19.612, p-value = 0.2676
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.31409194  0.09215861
## sample estimates:
## mean in group EC103 mean in group EC201 
##            1.599833            1.710800

• NBI

## 
##  Welch Two Sample t-test
## 
## data:  Parent$NBI by Parent$Tree.ID
## t = 0.47573, df = 14.7, p-value = 0.6413
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -5.076667  7.987334
## sample estimates:
## mean in group EC103 mean in group EC201 
##            33.14333            31.68800

Interesting sample pattern here, Chl and NBI start low and work high, Flav does the opposite. Maybe accuracy of measurements?

A Brief Look at Some Tree Data

## # A tibble: 6 x 5
##   Tree.ID   Chl   NBI   Anth  Flav
##   <fct>   <dbl> <dbl>  <dbl> <dbl>
## 1 IN4BT    34.5  16.2 0.110   2.17
## 2 IN4BV    27.5  13.8 0.121   2.01
## 3 IN4BW    24.8  12.5 0.127   1.99
## 4 IN4BX    37.6  18.4 0.0905  2.05
## 5 IN4BY    24.2  12.5 0.110   1.98
## 6 IN4BZ    32.0  15.6 0.106   2.09

Anthocyanin Overview

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: F1$Anth
##              Df Sum Sq   Mean Sq F value    Pr(>F)    
## F1$Tree.ID  158 0.5253 0.0033247  1.8093 2.001e-08 ***
## Residuals  1633 3.0007 0.0018376                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Chlorophyll Overview

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: F1$Chl
##              Df Sum Sq Mean Sq F value   Pr(>F)   
## F1$Tree.ID  158  47130  298.29  1.3395 0.004474 **
## Residuals  1633 363634  222.68                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Flavonol Overview

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: F1$Flav
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Tree.ID  158 25.118 0.15897  3.0531 < 2.2e-16 ***
## Residuals  1633 85.030 0.05207                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Nitrogen Overview

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: F1$NBI
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Tree.ID  158  16378 103.661  1.5147 8.435e-05 ***
## Residuals  1633 111761  68.439                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

A Closer Look at Invidual F1 Trees and Their Measurements

Msr = group_by(F1, Tree.ID, measure)
Msr = summarise(Msr, Anth = mean(Anth), Flav = mean(Flav), Chl = mean(Chl),NBI = mean(NBI))

#Select Random Column
#sample(1:4,10, replace = T)
#[1] 3 3 2 1 1 4 1 2 4 3

#Select Random Row
#sample(1:50,10, replace = T)
#[1] 34 37 44 20 44 47  9 19 22 40

F1 Height Analysis

## # A tibble: 3 x 5
##   Height   Anth   Chl  Flav   NBI
##   <fct>   <dbl> <dbl> <dbl> <dbl>
## 1 H      0.105   33.9  1.93  17.9
## 2 L      0.0968  35.6  1.98  18.5
## 3 M      0.0913  35.3  1.98  18.1

Height Measure Distributions

Anthocyanin

Chlorophyll

Flavonol

Nitrogen

ANOVAS

• Anthocyanin

## Analysis of Variance Table
## 
## Response: F1$Anth
##             Df Sum Sq   Mean Sq F value    Pr(>F)    
## F1$Height    2 0.0526 0.0262759  13.533 1.468e-06 ***
## Residuals 1789 3.4735 0.0019416                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = F1$Anth ~ F1$Height)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.10400 -0.02878 -0.00056  0.02666  0.37800 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.105002   0.001973  53.232  < 2e-16 ***
## F1$HeightL  -0.008225   0.002622  -3.137  0.00173 ** 
## F1$HeightM  -0.013666   0.002630  -5.197 2.26e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04406 on 1789 degrees of freedom
## Multiple R-squared:  0.0149, Adjusted R-squared:  0.0138 
## F-statistic: 13.53 on 2 and 1789 DF,  p-value: 1.468e-06

• Chlorophyll

## Analysis of Variance Table
## 
## Response: F1$Chl
##             Df Sum Sq Mean Sq F value Pr(>F)
## F1$Height    2    853  426.30  1.8605 0.1559
## Residuals 1789 409911  229.13

## 
## Call:
## lm(formula = F1$Chl ~ F1$Height)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.125 -11.129   1.178  11.731  25.998 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  33.9073     0.6776  50.038   <2e-16 ***
## F1$HeightL    1.6673     0.9006   1.851   0.0643 .  
## F1$HeightM    1.3481     0.9034   1.492   0.1358    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.14 on 1789 degrees of freedom
## Multiple R-squared:  0.002076,   Adjusted R-squared:  0.00096 
## F-statistic: 1.861 on 2 and 1789 DF,  p-value: 0.1559

• Flavonol

## Analysis of Variance Table
## 
## Response: F1$Flav
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## F1$Height    2   0.915 0.45758  7.4943 0.0005739 ***
## Residuals 1789 109.232 0.06106                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = F1$Flav ~ F1$Height)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9225 -0.1490  0.0170  0.1655  0.8775 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.93079    0.01106 174.548  < 2e-16 ***
## F1$HeightL   0.04770    0.01470   3.245  0.00120 ** 
## F1$HeightM   0.05272    0.01475   3.575  0.00036 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2471 on 1789 degrees of freedom
## Multiple R-squared:  0.008309,   Adjusted R-squared:  0.0072 
## F-statistic: 7.494 on 2 and 1789 DF,  p-value: 0.0005739

• NBI

## Analysis of Variance Table
## 
## Response: F1$NBI
##             Df Sum Sq Mean Sq F value Pr(>F)
## F1$Height    2    100  50.044  0.6992 0.4971
## Residuals 1789 128039  71.570

## 
## Call:
## lm(formula = F1$NBI ~ F1$Height)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.0776  -6.1206   0.3474   6.0613  31.0224 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  17.8703     0.3787  47.186   <2e-16 ***
## F1$HeightL    0.5912     0.5034   1.175    0.240    
## F1$HeightM    0.2772     0.5049   0.549    0.583    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.46 on 1789 degrees of freedom
## Multiple R-squared:  0.0007811,  Adjusted R-squared:  -0.000336 
## F-statistic: 0.6992 on 2 and 1789 DF,  p-value: 0.4971

Height Analysis within Trees

## # A tibble: 6 x 6
## # Groups:   Height [1]
##   Height Tree.ID   Anth   Chl  Flav   NBI
##   <fct>  <fct>    <dbl> <dbl> <dbl> <dbl>
## 1 H      IN4BT   0.116   43.6  2.09 21.1 
## 2 H      IN4BV   0.104   28.1  1.93 14.7 
## 3 H      IN4BW   0.12    18.5  2.06  9.15
## 4 H      IN4BX   0.0875  43.2  2.13 20.3 
## 5 H      IN4BY   0.121   27.7  1.96 14.3 
## 6 H      IN4BZ   0.0817  39.1  2.10 18.5

## Analysis of Variance Table
## 
## Response: High$Anth
##            Df   Sum Sq   Mean Sq F value  Pr(>F)   
## Low$Anth    1 0.009644 0.0096440  10.431 0.00151 **
## Residuals 157 0.145162 0.0009246                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = High$Anth ~ Low$Anth)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.082724 -0.020196 -0.001244  0.020111  0.095669 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.075038   0.009659   7.769 9.67e-13 ***
## Low$Anth    0.312539   0.096773   3.230  0.00151 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03041 on 157 degrees of freedom
## Multiple R-squared:  0.0623, Adjusted R-squared:  0.05632 
## F-statistic: 10.43 on 1 and 157 DF,  p-value: 0.00151

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$Anth
##            Df   Sum Sq    Mean Sq F value Pr(>F)
## Mid$Anth    1 0.001607 0.00160739  1.6473 0.2012
## Residuals 157 0.153198 0.00097579

## 
## Call:
## lm(formula = High$Anth ~ Mid$Anth)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.080176 -0.019699 -0.001994  0.017792  0.120025 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.09193    0.01067   8.616 6.97e-15 ***
## Mid$Anth     0.14627    0.11397   1.283    0.201    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03124 on 157 degrees of freedom
## Multiple R-squared:  0.01038,    Adjusted R-squared:  0.00408 
## F-statistic: 1.647 on 1 and 157 DF,  p-value: 0.2012

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: Mid$Anth
##            Df   Sum Sq    Mean Sq F value  Pr(>F)  
## Low$Anth    1 0.002597 0.00259684  5.6212 0.01896 *
## Residuals 157 0.072529 0.00046197                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Mid$Anth ~ Low$Anth)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.074218 -0.012195 -0.000834  0.013593  0.058269 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.075378   0.006828  11.040   <2e-16 ***
## Low$Anth    0.162181   0.068404   2.371    0.019 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02149 on 157 degrees of freedom
## Multiple R-squared:  0.03457,    Adjusted R-squared:  0.02842 
## F-statistic: 5.621 on 1 and 157 DF,  p-value: 0.01896

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$Chl
##            Df  Sum Sq Mean Sq F value Pr(>F)
## Low$Chl     1    40.6  40.577  0.4215 0.5171
## Residuals 157 15112.7  96.259

## 
## Call:
## lm(formula = High$Chl ~ Low$Chl)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.4732  -6.5662   0.8979   6.6457  24.2522 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 36.03022    3.39455  10.614   <2e-16 ***
## Low$Chl     -0.05995    0.09234  -0.649    0.517    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.811 on 157 degrees of freedom
## Multiple R-squared:  0.002678,   Adjusted R-squared:  -0.003675 
## F-statistic: 0.4215 on 1 and 157 DF,  p-value: 0.5171

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$Chl
##            Df  Sum Sq Mean Sq F value Pr(>F)
## Mid$Chl     1     6.5   6.517  0.0676 0.7953
## Residuals 157 15146.8  96.476

## 
## Call:
## lm(formula = High$Chl ~ Mid$Chl)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -24.3314  -6.5596   0.9516   7.1975  23.9071 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.75595    3.44048   10.10   <2e-16 ***
## Mid$Chl     -0.02468    0.09494   -0.26    0.795    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.822 on 157 degrees of freedom
## Multiple R-squared:  0.0004301,  Adjusted R-squared:  -0.005937 
## F-statistic: 0.06755 on 1 and 157 DF,  p-value: 0.7953

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: Mid$Chl
##            Df  Sum Sq Mean Sq F value Pr(>F)
## Low$Chl     1    86.5  86.465  1.2786 0.2599
## Residuals 157 10617.2  67.625

## 
## Call:
## lm(formula = Mid$Chl ~ Low$Chl)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.2237  -4.2267   0.5812   5.1386  17.4487 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 32.16619    2.84521  11.305   <2e-16 ***
## Low$Chl      0.08752    0.07740   1.131     0.26    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.223 on 157 degrees of freedom
## Multiple R-squared:  0.008078,   Adjusted R-squared:  0.00176 
## F-statistic: 1.279 on 1 and 157 DF,  p-value: 0.2599

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$Flav
##            Df  Sum Sq  Mean Sq F value   Pr(>F)   
## Low$Flav    1 0.15207 0.152067  7.9384 0.005462 **
## Residuals 157 3.00745 0.019156                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = High$Flav ~ Low$Flav)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69197 -0.07612  0.01771  0.09061  0.31947 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.59267    0.11926  13.355  < 2e-16 ***
## Low$Flav     0.16916    0.06004   2.818  0.00546 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1384 on 157 degrees of freedom
## Multiple R-squared:  0.04813,    Adjusted R-squared:  0.04207 
## F-statistic: 7.938 on 1 and 157 DF,  p-value: 0.005462

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$Flav
##            Df  Sum Sq Mean Sq F value    Pr(>F)    
## Mid$Flav    1 0.36919 0.36919  20.773 1.034e-05 ***
## Residuals 157 2.79032 0.01777                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = High$Flav ~ Mid$Flav)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69325 -0.06998  0.01107  0.09397  0.33382 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.30244    0.13749   9.473  < 2e-16 ***
## Mid$Flav     0.31517    0.06915   4.558 1.03e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1333 on 157 degrees of freedom
## Multiple R-squared:  0.1169, Adjusted R-squared:  0.1112 
## F-statistic: 20.77 on 1 and 157 DF,  p-value: 1.034e-05

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: Mid$Flav
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## Low$Flav    1 0.5438 0.54376  26.906 6.506e-07 ***
## Residuals 157 3.1729 0.02021                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Mid$Flav ~ Low$Flav)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.42522 -0.08825  0.00511  0.08340  0.47765 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.34975    0.12249  11.019  < 2e-16 ***
## Low$Flav     0.31987    0.06167   5.187 6.51e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1422 on 157 degrees of freedom
## Multiple R-squared:  0.1463, Adjusted R-squared:  0.1409 
## F-statistic: 26.91 on 1 and 157 DF,  p-value: 6.506e-07

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$NBI
##            Df Sum Sq Mean Sq F value Pr(>F)
## Low$NBI     1   12.2  12.156  0.4216 0.5171
## Residuals 157 4527.1  28.835

## 
## Call:
## lm(formula = High$NBI ~ Low$NBI)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.3802  -3.4352  -0.0889   3.7378  11.3144 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 18.88822    1.61024  11.730   <2e-16 ***
## Low$NBI     -0.05431    0.08365  -0.649    0.517    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.37 on 157 degrees of freedom
## Multiple R-squared:  0.002678,   Adjusted R-squared:  -0.003674 
## F-statistic: 0.4216 on 1 and 157 DF,  p-value: 0.5171

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: High$NBI
##            Df Sum Sq Mean Sq F value Pr(>F)
## Mid$NBI     1    5.6  5.6094  0.1943   0.66
## Residuals 157 4533.7 28.8769

## 
## Call:
## lm(formula = High$NBI ~ Mid$NBI)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.1320  -3.5765   0.0304   4.0196  11.0499 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 18.61881    1.72974  10.764   <2e-16 ***
## Mid$NBI     -0.04062    0.09217  -0.441     0.66    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.374 on 157 degrees of freedom
## Multiple R-squared:  0.001236,   Adjusted R-squared:  -0.005126 
## F-statistic: 0.1943 on 1 and 157 DF,  p-value: 0.66

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: Mid$NBI
##            Df Sum Sq Mean Sq F value  Pr(>F)  
## Low$NBI     1  106.0 105.990  5.0525 0.02598 *
## Residuals 157 3293.5  20.978                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Mid$NBI ~ Low$NBI)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.0884  -2.6169  -0.0763   2.5932  11.7726 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 15.21189    1.37343  11.076   <2e-16 ***
## Low$NBI      0.16038    0.07135   2.248    0.026 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.58 on 157 degrees of freedom
## Multiple R-squared:  0.03118,    Adjusted R-squared:  0.02501 
## F-statistic: 5.053 on 1 and 157 DF,  p-value: 0.02598

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Row Analysis

## # A tibble: 6 x 5
##   Row     Chl   NBI   Anth  Flav
##   <fct> <dbl> <dbl>  <dbl> <dbl>
## 1 1      35.6  17.3 0.107   2.09
## 2 10     30.5  15.7 0.112   1.98
## 3 11     29.9  15.0 0.112   2.04
## 4 12     34.6  18.7 0.0968  1.84
## 5 13     31.3  17.5 0.107   1.86
## 6 14     35.0  17.9 0.0888  1.98

##       Row         Chl             NBI             Anth       
##  17     :1   Min.   :32.13   Min.   :17.14   Min.   :0.1163  
##  0      :0   1st Qu.:32.13   1st Qu.:17.14   1st Qu.:0.1163  
##  1      :0   Median :32.13   Median :17.14   Median :0.1163  
##  10     :0   Mean   :32.13   Mean   :17.14   Mean   :0.1163  
##  11     :0   3rd Qu.:32.13   3rd Qu.:17.14   3rd Qu.:0.1163  
##  12     :0   Max.   :32.13   Max.   :17.14   Max.   :0.1163  
##  (Other):0                                                   
##       Flav      
##  Min.   :1.887  
##  1st Qu.:1.887  
##  Median :1.887  
##  Mean   :1.887  
##  3rd Qu.:1.887  
##  Max.   :1.887  
## 

##       Row          Chl             NBI             Anth        
##  1      : 1   Min.   :29.19   Min.   :14.38   Min.   :0.07868  
##  10     : 1   1st Qu.:32.02   1st Qu.:16.44   1st Qu.:0.08535  
##  11     : 1   Median :34.38   Median :17.81   Median :0.09354  
##  14     : 1   Mean   :34.97   Mean   :18.12   Mean   :0.09677  
##  15     : 1   3rd Qu.:37.05   3rd Qu.:19.46   3rd Qu.:0.10917  
##  16     : 1   Max.   :43.89   Max.   :23.16   Max.   :0.12239  
##  (Other):33                                                    
##       Flav      
##  Min.   :1.820  
##  1st Qu.:1.931  
##  Median :1.974  
##  Mean   :1.973  
##  3rd Qu.:2.037  
##  Max.   :2.092  
## 

##       Row         Chl             NBI             Anth        
##  12     :1   Min.   :31.33   Min.   :16.99   Min.   :0.08183  
##  13     :1   1st Qu.:34.20   1st Qu.:17.74   1st Qu.:0.09326  
##  23     :1   Median :35.08   Median :18.29   Median :0.09747  
##  32     :1   Mean   :35.09   Mean   :18.48   Mean   :0.09702  
##  41     :1   3rd Qu.:36.36   3rd Qu.:19.10   3rd Qu.:0.10265  
##  45     :1   Max.   :38.42   Max.   :20.71   Max.   :0.10721  
##  (Other):4                                                    
##       Flav      
##  Min.   :1.839  
##  1st Qu.:1.898  
##  Median :1.944  
##  Mean   :1.941  
##  3rd Qu.:1.995  
##  Max.   :2.032  
## 

## [1] 0.0001562666

## [1] 6.039853e-05

## [1] 14.76679

## [1] 4.10476

## [1] 0.004848629

## [1] 0.004125519

## [1] 5.602987

## [1] 1.155704

## 
##  Welch Two Sample t-test
## 
## data:  R4$Anth and R3$Anth
## t = 0.081174, df = 22.551, p-value = 0.936
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.006306855  0.006821440
## sample estimates:
##  mean of x  mean of y 
## 0.09702315 0.09676586

## 
##  Welch Two Sample t-test
## 
## data:  R4$Chl and R3$Chl
## t = 0.13309, df = 27.683, p-value = 0.8951
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.702350  1.938809
## sample estimates:
## mean of x mean of y 
##  35.08876  34.97053

## 
##  Welch Two Sample t-test
## 
## data:  R4$Flav and R3$Flav
## t = -1.3877, df = 14.921, p-value = 0.1856
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.08156262  0.01725693
## sample estimates:
## mean of x mean of y 
##  1.941185  1.973338

## 
##  Welch Two Sample t-test
## 
## data:  R4$Flav and R3$Flav
## t = -1.3877, df = 14.921, p-value = 0.1856
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.08156262  0.01725693
## sample estimates:
## mean of x mean of y 
##  1.941185  1.973338

Row Plots and ANOVAs

Anthocyanin

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Chlorophyll

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Flavonol

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Nitrogen

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: F1$Anth
##             Df Sum Sq   Mean Sq F value    Pr(>F)    
## F1$Row      49 0.2346 0.0047878  2.5339 4.261e-08 ***
## Residuals 1742 3.2914 0.0018895                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Chl
##             Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Row      49  21394  436.61  1.9533 0.0001046 ***
## Residuals 1742 389370  223.52                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Flav
##             Df  Sum Sq  Mean Sq F value   Pr(>F)    
## F1$Row      49   8.215 0.167646   2.865 3.11e-10 ***
## Residuals 1742 101.933 0.058515                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$NBI
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## F1$Row      49   7866 160.527   2.325 8.14e-07 ***
## Residuals 1742 120273  69.043                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Column Means

## # A tibble: 4 x 5
##   Column   Chl   NBI   Anth  Flav
##   <fct>  <dbl> <dbl>  <dbl> <dbl>
## 1 1       33.8  17.2 0.0945  2.01
## 2 2       35.4  18.6 0.0992  1.94
## 3 3       36.0  18.7 0.0990  1.96
## 4 4       34.3  18.7 0.0912  1.88

Data Overview of Column

##   0   1   2   3   4 
##   0 592 556 539 105

Column Boxplots

ANOVA

## Analysis of Variance Table
## 
## Response: F1$Anth
##             Df Sum Sq   Mean Sq F value Pr(>F)
## F1$Column    3 0.0122 0.0040655  2.0687 0.1024
## Residuals 1788 3.5138 0.0019652

## 
## Call:
## lm(formula = F1$Anth ~ F1$Column)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.09824 -0.02824 -0.00049  0.02676  0.38402 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.094490   0.001822  51.861   <2e-16 ***
## F1$Column2   0.004753   0.002618   1.815   0.0696 .  
## F1$Column3   0.004486   0.002639   1.700   0.0894 .  
## F1$Column4  -0.003337   0.004694  -0.711   0.4772    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04433 on 1788 degrees of freedom
## Multiple R-squared:  0.003459,   Adjusted R-squared:  0.001787 
## F-statistic: 2.069 on 3 and 1788 DF,  p-value: 0.1024

## Analysis of Variance Table
## 
## Response: F1$Chl
##             Df Sum Sq Mean Sq F value  Pr(>F)  
## F1$Column    3   1586  528.66  2.3101 0.07453 .
## Residuals 1788 409178  228.85                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = F1$Chl ~ F1$Column)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.263 -10.815   1.102  11.773  26.109 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  33.7951     0.6217  54.355   <2e-16 ***
## F1$Column2    1.5975     0.8934   1.788   0.0739 .  
## F1$Column3    2.2490     0.9006   2.497   0.0126 *  
## F1$Column4    0.4924     1.6019   0.307   0.7586    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.13 on 1788 degrees of freedom
## Multiple R-squared:  0.003861,   Adjusted R-squared:  0.00219 
## F-statistic:  2.31 on 3 and 1788 DF,  p-value: 0.07453

## Analysis of Variance Table
## 
## Response: F1$Flav
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## F1$Column    3   2.305 0.76823  12.737 3.087e-08 ***
## Residuals 1788 107.843 0.06031                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = F1$Flav ~ F1$Column)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.90465 -0.15390  0.00885  0.16468  0.85068 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.01032    0.01009 199.166  < 2e-16 ***
## F1$Column2  -0.06592    0.01450  -4.545 5.87e-06 ***
## F1$Column3  -0.04967    0.01462  -3.397 0.000695 ***
## F1$Column4  -0.13528    0.02601  -5.202 2.20e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2456 on 1788 degrees of freedom
## Multiple R-squared:  0.02092,    Adjusted R-squared:  0.01928 
## F-statistic: 12.74 on 3 and 1788 DF,  p-value: 3.087e-08

## Analysis of Variance Table
## 
## Response: F1$NBI
##             Df Sum Sq Mean Sq F value   Pr(>F)   
## F1$Column    3    821 273.626  3.8427 0.009333 **
## Residuals 1788 127318  71.207                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = F1$NBI ~ F1$Column)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -18.560  -6.118   0.291   6.107  31.944 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  17.2255     0.3468  49.667  < 2e-16 ***
## F1$Column2    1.3478     0.4983   2.705  0.00690 ** 
## F1$Column3    1.5184     0.5024   3.022  0.00254 ** 
## F1$Column4    1.4342     0.8936   1.605  0.10866    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.438 on 1788 degrees of freedom
## Multiple R-squared:  0.006406,   Adjusted R-squared:  0.004739 
## F-statistic: 3.843 on 3 and 1788 DF,  p-value: 0.009333

## Analysis of Variance Table
## 
## Response: F1$Anth
##                              Df  Sum Sq   Mean Sq F value    Pr(>F)    
## F1$Height                     2 0.05255 0.0262759 14.9537 3.788e-07 ***
## F1$Column                     3 0.01228 0.0040942  2.3300 0.0727244 .  
## F1$Row                       49 0.23127 0.0047199  2.6861 6.175e-09 ***
## F1$Height:F1$Column           6 0.02055 0.0034247  1.9490 0.0699958 .  
## F1$Height:F1$Row             98 0.20024 0.0020433  1.1628 0.1394606    
## F1$Column:F1$Row            106 0.28473 0.0026861  1.5287 0.0006952 ***
## F1$Height:F1$Column:F1$Row  212 0.41375 0.0019517  1.1107 0.1490621    
## Residuals                  1315 2.31066 0.0017572                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Anth
##                    Df  Sum Sq   Mean Sq F value    Pr(>F)    
## F1$Height           2 0.05255 0.0262759 14.2135 7.586e-07 ***
## F1$Row             49 0.23404 0.0047763  2.5837 2.178e-08 ***
## F1$Height:F1$Row   98 0.20394 0.0020810  1.1257    0.1942    
## Residuals        1642 3.03551 0.0018487                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Chl
##                              Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Height                     2    853  426.30  2.0422  0.130152    
## F1$Column                     3   1577  525.57  2.5178  0.056677 .  
## F1$Row                       49  21813  445.16  2.1326 1.244e-05 ***
## F1$Height:F1$Column           6   1282  213.61  1.0233  0.408244    
## F1$Height:F1$Row             98  27033  275.85  1.3215  0.022708 *  
## F1$Column:F1$Row            106  24037  226.77  1.0863  0.265386    
## F1$Height:F1$Column:F1$Row  212  59670  281.46  1.3484  0.001427 ** 
## Residuals                  1315 274499  208.74                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Chl
##                    Df Sum Sq Mean Sq F value   Pr(>F)    
## F1$Height           2    853  426.30  1.9372  0.14444    
## F1$Row             49  21279  434.27  1.9734 8.34e-05 ***
## F1$Height:F1$Row   98  27286  278.43  1.2652  0.04464 *  
## Residuals        1642 361346  220.06                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Chl
##             Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Row      49  21394  436.61  1.9533 0.0001046 ***
## Residuals 1742 389370  223.52                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$Flav
##                              Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Height                     2  0.915 0.45758  9.3660 9.143e-05 ***
## F1$Column                     3  2.323 0.77447 15.8523 3.957e-10 ***
## F1$Row                       49  8.139 0.16611  3.4001 1.213e-13 ***
## F1$Height:F1$Column           6  1.004 0.16728  3.4240  0.002334 ** 
## F1$Height:F1$Row             98  5.743 0.05860  1.1995  0.096365 .  
## F1$Column:F1$Row            106 14.790 0.13953  2.8559 < 2.2e-16 ***
## F1$Height:F1$Column:F1$Row  212 12.988 0.06126  1.2540  0.012358 *  
## Residuals                  1315 64.245 0.04886                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$NBI
##                              Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Height                     2    100  50.044  0.7850 0.4563286    
## F1$Column                     3    818 272.802  4.2793 0.0051365 ** 
## F1$Row                       49   7816 159.511  2.5021 8.551e-08 ***
## F1$Height:F1$Column           6    792 132.004  2.0707 0.0539220 .  
## F1$Height:F1$Row             98   8175  83.418  1.3085 0.0268723 *  
## F1$Column:F1$Row            106   7765  73.250  1.1490 0.1510179    
## F1$Height:F1$Column:F1$Row  212  18842  88.877  1.3942 0.0004396 ***
## Residuals                  1315  83831  63.750                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: F1$NBI
##                    Df Sum Sq Mean Sq F value    Pr(>F)    
## F1$Row             49   7866 160.527  2.3456 6.383e-07 ***
## F1$Column           3    789 263.021  3.8432   0.00934 ** 
## F1$Row:F1$Column  106   7724  72.864  1.0647   0.31303    
## Residuals        1633 111761  68.439                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Controlling for Height,Column,Row effects

Dat = F1

#Identifying outliers outside 
OBA <-boxplot(Dat$Anth,range = 3.5, plot = F)$out
OBC <-boxplot(Dat$Chl,range = 3, plot = F)$out
OBF <-boxplot(Dat$Flav,range = 3, plot = F)$out
OBN <-boxplot(Dat$NBI,range = 3,plot=F)$out

#Isolating outliers exceeding
OA = Dat[which(Dat$Anth %in% OBA),];OA

##     Collection.Day Allocation Block Column Row group Group.ID Tree.ID Rep.
## 605              3         F1    34      3  17    38      116   IN4FM    N
## 694              2         F1    10      2  20    33       69   IN4E4    N
##     measure Height Flower    Chl  Flav  Anth   NBI
## 605      11      H      N 59.122 1.640 0.483 36.05
## 694       7      M      N 18.511 1.401 0.370 13.21

OC = Dat[which(Dat$Anth %in% OBC),];OC

##  [1] Collection.Day Allocation     Block          Column        
##  [5] Row            group          Group.ID       Tree.ID       
##  [9] Rep.           measure        Height         Flower        
## [13] Chl            Flav           Anth           NBI           
## <0 rows> (or 0-length row.names)

OF = Dat[which(Dat$Anth %in% OBF),];OF

##  [1] Collection.Day Allocation     Block          Column        
##  [5] Row            group          Group.ID       Tree.ID       
##  [9] Rep.           measure        Height         Flower        
## [13] Chl            Flav           Anth           NBI           
## <0 rows> (or 0-length row.names)

ON = Dat[which(Dat$Anth %in% OBN),];ON

##  [1] Collection.Day Allocation     Block          Column        
##  [5] Row            group          Group.ID       Tree.ID       
##  [9] Rep.           measure        Height         Flower        
## [13] Chl            Flav           Anth           NBI           
## <0 rows> (or 0-length row.names)

Dat <- Dat[-which(Dat$Anth %in% OBA),]

DATG <- ggplot(F1) + aes(x = Tree.ID, y = Anth,) + geom_boxplot(fill = "dodgerblue1", size = 1.25) + ylab("Anth") + xlab("Tree ID") + ggtitle("Anthocyanin Raw Data") +stat_summary(fun.y=mean, colour="gray90", geom="point", shape=18, size=3) +theme_bw()+theme(plot.title = element_text(hjust = 0.5))+geom_hline(yintercept = mean(F1$Anth))

DATG2 <- ggplot(Dat) + aes(x = Tree.ID, y = Anth,) + geom_boxplot(fill = "dodgerblue1", size = 1.25) + ylab("Anth") + xlab("Tree ID") + ggtitle("Anthocyanin Outliers Removed") +stat_summary(fun.y=mean, colour="gray90", geom="point", shape=18, size=3) +theme_bw()+theme(plot.title = element_text(hjust = 0.5))+geom_hline(yintercept = mean(Dat$Anth))

grid.arrange(DATG,DATG2)

#Total Mean
Dat$ATmean = mean(Dat$Anth)
Dat$CTmean = mean(Dat$Chl)
Dat$FTmean = mean(Dat$Flav)
Dat$NTmean = mean(Dat$NBI)

#Remove Total Mean
Dat$Anth2 = Dat$Anth - Dat$ATmean
Dat$Chl2 = Dat$Chl - Dat$CTmean
Dat$Flav2 = Dat$Flav - Dat$FTmean
Dat$NBI2 = Dat$NBI - Dat$NTmean

#Height Mean for Anth and Flav
DatH = group_by(Dat, Height)
DatH = summarise(DatH, HAnth = mean(Anth, na.rm = T), HChl = mean(Chl, na.rm =T), HFlav = mean(Flav,na.rm = T), HNBI = mean(NBI, na.rm = T))

#Add Height Mean to Data
Dat =merge(Dat, DatH, by.x = "Height")

#Calculate Height Mean Deviation from Total Mean 
Dat$ATH = Dat$ATmean - Dat$HAnth
Dat$CTH = Dat$CTmean - Dat$HChl
Dat$FTH = Dat$FTmean - Dat$HFlav
Dat$NTH = Dat$NTmean - Dat$HNBI

#Controlling for Height Anth and Flav
Dat$Anth3 = Dat$Anth2 + Dat$ATH
Dat$Chl3 = Dat$Chl2 + Dat$CTH
Dat$Flav3 = Dat$Flav2 + Dat$FTH
Dat$NBI3 = Dat$NBI2 + Dat$NTH

#Column Mean for Chl, Flav,NBI
DatC = group_by(Dat, Column)
DatC = summarise(DatC, CAnth = mean(Anth, na.rm = T), CChl = mean(Chl, na.rm = T) ,CFlav = mean(Flav,na.rm = T), CNBI = mean(NBI,na.rm = T))

#Add Column Mean to Data
Dat =merge(Dat, DatC, by.x = "Column")

#Calculate Column Mean Deviation from Total Mean
Dat$ATC = Dat$ATmean - Dat$CAnth
Dat$CTC = Dat$CTmean - Dat$CChl
Dat$FTC = Dat$FTmean - Dat$CFlav
Dat$NTC = Dat$NTmean - Dat$CNBI

#Controlling for Column Chl, Flav and NBI
Dat$Anth4 = Dat$Anth3 + Dat$ATC
Dat$Chl4 = Dat$Chl2 + Dat$CTC
Dat$Flav4 = Dat$Flav3 + Dat$FTC
Dat$NBI4 = Dat$NBI3 + Dat$NTC

#Row Mean for Anth, Chl, Flav and and NBI
DatR = group_by(Dat, Row)
DatR = summarise(DatR, RAnth = mean(Anth,na.rm = T),RChl = mean(Chl,na.rm = T), RFlav = mean(Flav,na.rm = T), RNBI = mean(NBI,na.rm = T))

#Add Row Mean to Data
Dat =merge(Dat, DatR, by.x = "Row")

#Calculate Row Mean Deviation from Total Mean 
Dat$ATR = Dat$ATmean - Dat$RAnth
Dat$CTR = Dat$CTmean - Dat$RChl
Dat$FTR = Dat$FTmean - Dat$RFlav
Dat$NTR = Dat$NTmean - Dat$RNBI

#Controlling for Row in Anth, Chl, Flav and NBI
Dat$Anth5 = Dat$Anth4 + Dat$ATR
Dat$Chl5 = Dat$Chl4 + Dat$CTR
Dat$Flav5 = Dat$Flav4 + Dat$FTR
Dat$NBI5 = Dat$NBI4 + Dat$NTR

New ANOVAs

## Analysis of Variance Table
## 
## Response: Dat$Anth5
##                                 Df  Sum Sq   Mean Sq F value  Pr(>F)    
## Dat$Height                       2 0.00000 0.0000013  0.0008 0.99918    
## Dat$Column                       3 0.00043 0.0001418  0.0869 0.96722    
## Dat$Row                         49 0.00058 0.0000118  0.0072 1.00000    
## Dat$Height:Dat$Column            6 0.01972 0.0032863  2.0144 0.06088 .  
## Dat$Height:Dat$Row              98 0.18437 0.0018813  1.1532 0.15291    
## Dat$Column:Dat$Row             106 0.26715 0.0025203  1.5448 0.00052 ***
## Dat$Height:Dat$Column:Dat$Row  212 0.41022 0.0019350  1.1861 0.04567 *  
## Residuals                     1313 2.14207 0.0016314                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Dat$Chl5
##                                 Df Sum Sq Mean Sq F value   Pr(>F)   
## Dat$Height                       2    791  395.31  1.8944 0.150825   
## Dat$Column                       3    197   65.56  0.3142 0.815149   
## Dat$Row                         49    156    3.19  0.0153 1.000000   
## Dat$Height:Dat$Column            6   1277  212.78  1.0196 0.410662   
## Dat$Height:Dat$Row              98  26884  274.33  1.3146 0.024850 * 
## Dat$Column:Dat$Row             106  23892  225.40  1.0801 0.279036   
## Dat$Height:Dat$Column:Dat$Row  212  59481  280.57  1.3445 0.001572 **
## Residuals                     1313 273994  208.68                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Dat$Flav5
##                                 Df Sum Sq  Mean Sq F value    Pr(>F)    
## Dat$Height                       2  0.001 0.000562  0.0115  0.988538    
## Dat$Column                       3  0.011 0.003615  0.0742  0.973871    
## Dat$Row                         49  0.214 0.004364  0.0895  1.000000    
## Dat$Height:Dat$Column            6  1.000 0.166608  3.4182  0.002368 ** 
## Dat$Height:Dat$Row              98  5.708 0.058249  1.1951  0.100948    
## Dat$Column:Dat$Row             106 14.742 0.139078  2.8534 < 2.2e-16 ***
## Dat$Height:Dat$Column:Dat$Row  212 12.986 0.061253  1.2567  0.011685 *  
## Residuals                     1313 63.997 0.048741                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Dat$NBI5
##                                 Df Sum Sq Mean Sq F value   Pr(>F)    
## Dat$Height                       2      3   1.352  0.0212 0.978979    
## Dat$Column                       3     50  16.825  0.2644 0.851104    
## Dat$Row                         49     22   0.453  0.0071 1.000000    
## Dat$Height:Dat$Column            6    795 132.483  2.0816 0.052659 .  
## Dat$Height:Dat$Row              98   8157  83.239  1.3079 0.027100 *  
## Dat$Column:Dat$Row             106   7730  72.925  1.1458 0.155856    
## Dat$Height:Dat$Column:Dat$Row  212  18762  88.498  1.3905 0.000485 ***
## Residuals                     1313  83565  63.644                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparison Heatmaps

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

## Analysis of Variance Table
## 
## Response: Anth5
##                   Df  Sum Sq Mean Sq  F value    Pr(>F)    
## Chl5               1 0.32495 0.32495 225.0996 < 2.2e-16 ***
## Flav5              1 0.06820 0.06820  47.2416 8.648e-12 ***
## NBI5               1 0.02278 0.02278  15.7770 7.410e-05 ***
## Chl5:Flav5         1 0.00951 0.00951   6.5852   0.01036 *  
## Chl5:NBI5          1 0.02430 0.02430  16.8357 4.260e-05 ***
## Flav5:NBI5         1 0.00218 0.00218   1.5087   0.21950    
## Chl5:Flav5:NBI5    1 0.00016 0.00016   0.1093   0.74100    
## Residuals       1782 2.57247 0.00144                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Chl5
##                    Df Sum Sq Mean Sq    F value Pr(>F)    
## Anth5               1  41543   41543 2.5419e+04 <2e-16 ***
## Flav5               1    202     202 1.2366e+02 <2e-16 ***
## NBI5                1 335250  335250 2.0513e+05 <2e-16 ***
## Anth5:Flav5         1    494     494 3.0218e+02 <2e-16 ***
## Anth5:NBI5          1    167     167 1.0217e+02 <2e-16 ***
## Flav5:NBI5          1   6102    6102 3.7336e+03 <2e-16 ***
## Anth5:Flav5:NBI5    1      0       0 1.5590e-01  0.693    
## Residuals        1782   2912       2                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Flav5
##                   Df Sum Sq Mean Sq   F value    Pr(>F)    
## Anth5              1  3.055   3.055  265.2320 < 2.2e-16 ***
## Chl5               1  0.056   0.056    4.8612   0.02759 *  
## NBI5               1 74.121  74.121 6435.9193 < 2.2e-16 ***
## Anth5:Chl5         1  0.522   0.522   45.3622 2.203e-11 ***
## Anth5:NBI5         1  0.178   0.178   15.4884 8.620e-05 ***
## Chl5:NBI5          1  0.204   0.204   17.7366 2.664e-05 ***
## Anth5:Chl5:NBI5    1  0.000   0.000    0.0127   0.91035    
## Residuals       1782 20.523   0.012                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: NBI5
##                    Df Sum Sq Mean Sq    F value Pr(>F)    
## Anth5               1  13748   13748 2.0883e+04 <2e-16 ***
## Chl5                1  93493   93493 1.4201e+05 <2e-16 ***
## Flav5               1   9187    9187 1.3954e+04 <2e-16 ***
## Anth5:Chl5          1     49      49 7.4257e+01 <2e-16 ***
## Anth5:Flav5         1    103     103 1.5674e+02 <2e-16 ***
## Chl5:Flav5          1   1331    1331 2.0210e+03 <2e-16 ***
## Anth5:Chl5:Flav5    1      0       0 2.4100e-02 0.8768    
## Residuals        1782   1173       1                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: Dat$Anth5
##              Df  Sum Sq    Mean Sq F value Pr(>F)
## Dat$Flower    1 0.00036 0.00036392  0.2152 0.6428
## Residuals  1788 3.02417 0.00169137

## 
## Call:
## lm(formula = Dat$Anth5 ~ Dat$Flower)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.105618 -0.028027 -0.000984  0.025667  0.201307 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0002807  0.0011451  -0.245    0.806
## Dat$FlowerY  0.0010050  0.0021665   0.464    0.643
## 
## Residual standard error: 0.04113 on 1788 degrees of freedom
## Multiple R-squared:  0.0001203,  Adjusted R-squared:  -0.0004389 
## F-statistic: 0.2152 on 1 and 1788 DF,  p-value: 0.6428

## Analysis of Variance Table
## 
## Response: Dat$Chl5
##              Df Sum Sq Mean Sq F value Pr(>F)
## Dat$Flower    1     19  18.847  0.0872 0.7679
## Residuals  1788 386652 216.248

## 
## Call:
## lm(formula = Dat$Chl5 ~ Dat$Flower)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.009 -10.634   1.455  11.317  31.370 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.06388    0.40943  -0.156    0.876
## Dat$FlowerY  0.22870    0.77468   0.295    0.768
## 
## Residual standard error: 14.71 on 1788 degrees of freedom
## Multiple R-squared:  4.874e-05,  Adjusted R-squared:  -0.0005105 
## F-statistic: 0.08716 on 1 and 1788 DF,  p-value: 0.7679

## Analysis of Variance Table
## 
## Response: Dat$Flav5
##              Df Sum Sq  Mean Sq F value  Pr(>F)  
## Dat$Flower    1  0.245 0.244694  4.4456 0.03513 *
## Residuals  1788 98.414 0.055042                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Call:
## lm(formula = Dat$Flav5 ~ Dat$Flower)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.86910 -0.14463  0.01577  0.15365  0.80773 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.007279   0.006532  -1.114   0.2653  
## Dat$FlowerY  0.026059   0.012359   2.108   0.0351 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2346 on 1788 degrees of freedom
## Multiple R-squared:  0.00248,    Adjusted R-squared:  0.001922 
## F-statistic: 4.446 on 1 and 1788 DF,  p-value: 0.03513

## Analysis of Variance Table
## 
## Response: Dat$NBI5
##              Df Sum Sq Mean Sq F value Pr(>F)
## Dat$Flower    1     13  13.012  0.1954 0.6585
## Residuals  1788 119071  66.595

## 
## Call:
## lm(formula = Dat$NBI5 ~ Dat$Flower)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -20.4419  -5.8719   0.2175   5.8066  28.8506 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.05308    0.22721   0.234    0.815
## Dat$FlowerY -0.19003    0.42990  -0.442    0.659
## 
## Residual standard error: 8.161 on 1788 degrees of freedom
## Multiple R-squared:  0.0001093,  Adjusted R-squared:  -0.00045 
## F-statistic: 0.1954 on 1 and 1788 DF,  p-value: 0.6585

## Warning: NAs introduced by coercion

## Analysis of Variance Table
## 
## Response: H089$Anth
##            Df   Sum Sq    Mean Sq F value Pr(>F)
## H089$Diff   1 0.000292 0.00029205  1.0337 0.3109
## Residuals 149 0.042094 0.00028251

## Analysis of Variance Table
## 
## Response: H089$Anth
##                Df   Sum Sq    Mean Sq F value Pr(>F)  
## H089$Height08   1 0.001142 0.00114216  4.1262  0.044 *
## Residuals     149 0.041244 0.00027681                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$Anth
##                Df   Sum Sq    Mean Sq F value  Pr(>F)  
## H089$Height09   1 0.001706 0.00170619  6.2493 0.01351 *
## Residuals     149 0.040680 0.00027302                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$Chl
##            Df Sum Sq Mean Sq F value Pr(>F)
## H089$Diff   1    0.9  0.9142  0.0332 0.8556
## Residuals 149 4099.2 27.5113

## Analysis of Variance Table
## 
## Response: H089$Chl
##                Df Sum Sq Mean Sq F value   Pr(>F)   
## H089$Height08   1  201.5 201.535  7.7025 0.006222 **
## Residuals     149 3898.6  26.165                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$Chl
##                Df Sum Sq Mean Sq F value  Pr(>F)  
## H089$Height09   1  177.8 177.810  6.7547 0.01029 *
## Residuals     149 3922.3  26.324                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$Flav
##            Df  Sum Sq  Mean Sq F value  Pr(>F)  
## H089$Diff   1 0.03732 0.037322  4.3811 0.03803 *
## Residuals 149 1.26932 0.008519                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$Flav
##                Df  Sum Sq   Mean Sq F value Pr(>F)
## H089$Height08   1 0.01095 0.0109540  1.2597 0.2635
## Residuals     149 1.29569 0.0086959

## Analysis of Variance Table
## 
## Response: H089$Flav
##                Df  Sum Sq   Mean Sq F value Pr(>F)
## H089$Height09   1 0.00096 0.0009574  0.1093 0.7415
## Residuals     149 1.30568 0.0087630

## Analysis of Variance Table
## 
## Response: H089$NBI
##            Df  Sum Sq Mean Sq F value Pr(>F)
## H089$Diff   1    6.38  6.3824  0.6957 0.4056
## Residuals 149 1366.93  9.1740

## Analysis of Variance Table
## 
## Response: H089$NBI
##                Df  Sum Sq Mean Sq F value  Pr(>F)  
## H089$Height08   1   29.09 29.0855   3.224 0.07459 .
## Residuals     149 1344.22  9.0216                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H089$NBI
##                Df  Sum Sq Mean Sq F value  Pr(>F)  
## H089$Height09   1   41.76  41.757  4.6726 0.03224 *
## Residuals     149 1331.55   8.937                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: H0892$Height08
##            Df Sum Sq Mean Sq F value   Pr(>F)   
## H0892$Row  49  48775  995.40  1.9908 0.001269 **
## Residuals 121  60501  500.01                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Height09
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## H0892$Row  49  62417 1273.82  2.0535 0.0007953 ***
## Residuals 121  75058  620.32                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Diff
##            Df Sum Sq Mean Sq F value Pr(>F)
## H0892$Row  49  12742  260.04  0.7015 0.9197
## Residuals 121  44853  370.69

## Analysis of Variance Table
## 
## Response: H0892$Height08
##               Df Sum Sq Mean Sq F value    Pr(>F)    
## H0892$Column   3  30712 10237.3  21.761 6.033e-12 ***
## Residuals    167  78564   470.4                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Height09
##               Df Sum Sq Mean Sq F value    Pr(>F)    
## H0892$Column   3  49883 16627.8  31.702 2.842e-16 ***
## Residuals    167  87592   524.5                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Diff
##               Df Sum Sq Mean Sq F value  Pr(>F)  
## H0892$Column   3   3480 1159.90  3.5794 0.01519 *
## Residuals    167  54115  324.04                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Analysis of Variance Table
## 
## Response: H0892$Height08
##            Df Sum Sq Mean Sq F value   Pr(>F)   
## H0892$Row  49  48775  995.40  1.9908 0.001269 **
## Residuals 121  60501  500.01                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Height09
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## H0892$Row  49  62417 1273.82  2.0535 0.0007953 ***
## Residuals 121  75058  620.32                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: H0892$Diff
##            Df Sum Sq Mean Sq F value Pr(>F)
## H0892$Row  49  12742  260.04  0.7015 0.9197
## Residuals 121  44853  370.69

## Analysis of Variance Table
## 
## Response: HData$F8
##               Df Sum Sq Mean Sq F value  Pr(>F)  
## HData$Column   3   2427  809.10   3.181 0.02546 *
## Residuals    167  42477  254.35                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: HData$F9
##               Df Sum Sq Mean Sq F value   Pr(>F)   
## HData$Column   3   3731 1243.57  4.7497 0.003321 **
## Residuals    167  43724  261.82                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Analysis of Variance Table
## 
## Response: HData$FDiff
##               Df Sum Sq Mean Sq F value Pr(>F)
## HData$Column   3    150  50.054  0.1985 0.8973
## Residuals    167  42111 252.161